Question

Young's double slit experiment is first performed in air and then in a medium other than air. It is found that $8^{th}$ bright fringe in the medium lies where $5^{th}$ dark fringe lies in air. The refractive index of the medium is nearly:

• A. 1.78
• B. 1.25
• C. 1.59
• D. 1.69

Answer 1

Answer: (A)

1.78

In medium ${\lambda }_{medium}=\frac{{\lambda }_{air}}{\mu }$
${\lambda }^{\prime }=\frac{\lambda }{\mu }$

For Air, $5^{th}$ dark,
$y_s=(2m-1)\frac{\lambda D}{2d}$
$m=5$,

$y_s=\frac{9\lambda D}{2d}$

For bright in medium m
$y^{\prime }=n\frac{{\lambda }^{\prime }D}{d}$, ${\lambda }^{\prime }=\frac{\lambda }{\mu }$

$\therefore y^{\prime }=\frac{8\lambda }{\mu }\frac{D}{d}$

$y^{\prime }=y$

$\frac{9\times D}{2d}=\frac{8\times D}{\mu d}$

$\therefore \mu =\frac{8\times 2}{9}$

$\mu =1.78$